List questions from cauchy-schwarz-inequality

Published on 25 Mar 2026 - 9:33

93

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Prove that $\frac{x^{2}}{(x-y)^{2}}+\frac{y^{2}}{(y-z)^{2}}+\frac{z^{2}}{(z-x)^{2}} \geq 1$

Published on 28 Mar 2026 - 7:15

65

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Is there any constant $c$ satisfying the inequality

Published on 02 May 2020 - 8:06

157

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If $x+y+z=1$ Find the maximum of $\frac{x-y}{\sqrt{x+y}}+\frac{y-z}{\sqrt{y+z}}+\frac{z-x}{\sqrt{z+x}}$

Published on 02 May 2020 - 11:58

112

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Does this 2-norm inequality hold?

Published on 02 May 2020 - 21:20

137

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How can I approach this inequality?

Published on 25 Mar 2026 - 14:20

818

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Using Cauchy-Schwarz to prove the triangle inequality

Published on 05 May 2020 - 0:57

151

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Prove that $\sqrt{\frac{2 a^{2}+b c}{a^{2}+2 b c}}+\sqrt{\frac{2 b^{2}+c a}{b^{2}+2 c a}}+\sqrt{\frac{2 c^{2}+a b}{c^{2}+2 a b}} \geq 2 \sqrt{2}$

Published on 28 Mar 2026 - 7:15

134

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If $x+y+z=1$ prove $ \sqrt{x+\frac{(y-z)^{2}}{12}}+\sqrt{y+\frac{(z-x)^{2}}{12}}+\sqrt{z+\frac{(x-y)^{2}}{12}} \leq \sqrt{3} $

Published on 25 Mar 2026 - 19:07

187

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If $a+b+c+d=4$ Prove that $ \sqrt{\frac{a+1}{a b+1}}+\sqrt{\frac{b+1}{b c+1}}+\sqrt{\frac{c+1}{c d+1}}+\sqrt{\frac{d+1}{d a+1}} \geq 4 $

Published on 25 Mar 2026 - 16:20

154

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Prove that $\frac{1}{1 - \sqrt{ab}} + \frac{1}{1 - \sqrt{bc}} + \frac{1}{1 - \sqrt{ca}} \leq \frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}$

Published on 28 Mar 2026 - 7:15

113

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Olympiad Inequality: Cauchy Schwartz

Published on 25 Mar 2026 - 16:13

176

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Application of Cauchy-Schwarz to sum of expected values

Published on 12 May 2020 - 13:54

194

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Maximize $a^T x$ with constraint on $2$-norm of $x$

Published on 13 May 2020 - 14:06

37

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Inequality Integral who involves logarithms and exponentials

Published on 26 Mar 2026 - 22:50

List Question

Stuck when transforming and solving this

Prove that $\frac{x^{2}}{(x-y)^{2}}+\frac{y^{2}}{(y-z)^{2}}+\frac{z^{2}}{(z-x)^{2}} \geq 1$

Is there any constant $c$ satisfying the inequality

If $x+y+z=1$ Find the maximum of $\frac{x-y}{\sqrt{x+y}}+\frac{y-z}{\sqrt{y+z}}+\frac{z-x}{\sqrt{z+x}}$

Does this 2-norm inequality hold?

How can I approach this inequality?

Using Cauchy-Schwarz to prove the triangle inequality

Prove that $\sqrt{\frac{2 a^{2}+b c}{a^{2}+2 b c}}+\sqrt{\frac{2 b^{2}+c a}{b^{2}+2 c a}}+\sqrt{\frac{2 c^{2}+a b}{c^{2}+2 a b}} \geq 2 \sqrt{2}$

If $x+y+z=1$ prove $ \sqrt{x+\frac{(y-z)^{2}}{12}}+\sqrt{y+\frac{(z-x)^{2}}{12}}+\sqrt{z+\frac{(x-y)^{2}}{12}} \leq \sqrt{3} $

If $a+b+c+d=4$ Prove that $ \sqrt{\frac{a+1}{a b+1}}+\sqrt{\frac{b+1}{b c+1}}+\sqrt{\frac{c+1}{c d+1}}+\sqrt{\frac{d+1}{d a+1}} \geq 4 $

Prove that $\frac{1}{1 - \sqrt{ab}} + \frac{1}{1 - \sqrt{bc}} + \frac{1}{1 - \sqrt{ca}} \leq \frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}$

Olympiad Inequality: Cauchy Schwartz

Application of Cauchy-Schwarz to sum of expected values

Maximize $a^T x$ with constraint on $2$-norm of $x$

Inequality Integral who involves logarithms and exponentials

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